
As in [1]}, the approximate rarefaction wave to the
compressible Navier-Stokes equations (REF ) can be constructed
by the solution of the Burgers equation
\(\left\lbrace \begin{array}{l}\displaystyle w_{t}+ww_{x}=0,\\\displaystyle w( 0,x)=w_\delta (x)=w(\frac{x}{\delta })=\frac{w_++w_-}{2}+\frac{w_+-w_-}{2}\tanh \frac{x}{\delta },\end{array}\right.\) 
